a) \frac{12}{7}

b) \frac{11}{9}

c) \frac{5}{7}

d) \frac{19}{13}

correct answer is: a) \frac{12}{7}

correct answer is:

Explanation

The given expression is:
32^{2x-5} = 4 \times 8^{x-5}
\rightarrow(2^5)^{2x-5} = 4 \times (2^3)^{x-5}
\rightarrow2^{5(2x-5)} = 4 \times 2^{3(x-5)}
\rightarrow2^{10x - 25} = 4 \times 2^{3x - 15}
\rightarrow2^{10x - 25} = 2^2 \times 2^{3x - 15}
\rightarrow2^{10x - 25} = 2^{2 + 3x - 15}
Since the bases are the same, we can equate the exponents:
\rightarrow10x - 25 = 2 + 3x - 15
\rightarrow10x - 25 = 3x - 13
\rightarrow10x - 3x = 25 - 13
\rightarrow7x = 12
\rightarrow x=\frac{12}7
Ans: The value of x is \frac{12}{7} .